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~ :,i.9

O

I 7

i

2.8 3.2 3.6 4.0Wavelength (Jlm)

FlI' 2 The 2.0-4.0 J.LIIl spectrum o IRS7. The solid curve is theestimated position of the continuum (see text). The dashed curve isthe July 1980 spectrum where it deviates from 'lhe May 1981

spectrum.

bands stretching from 2.9 to 3.6 J.Lm.Two dominant bands lie at3.03 and 3.40 J.Lm,and have optical depths of 0.41 and 0.32respectively. The increased optical depth of the 3.4 J.Lmfeaturerelative to our previous resultl reflects the improved definitionof the continuum. This optical depth would be further increasedf the redness between 3.6 and 3.95 11mwere due to absorption

rather than to the addition of cool dust.Figure 2 shows ali of the absorption features we believe to be

real, and a few (marked?) which are less certaiu. The abtorptionclearly breaks up into many discrete features and two of these (at3.192 and 3.295 J.Lm)are quite narrow. Whilst the broad fea-tures centred at 3.03 J.Lmand 3.40 J.Lmpresumably arise in solidgrains, the narrow features may have a gaseous origino We havefound no convincing identification for either, although manyhydrocarbons have stretching absorptions in this spectral range.However, laboratory data are not available for even quitesimple, incompletely bonded molecules (for example CH3) suchas might be found in the interstellar environment. Quite narrow

absorption bands are found in the absorption spectra of somesolids, such as methane4 and methyI alcohol'.

Suitable data on the absorption properties of solid materiaIsare not available, and laboratory work is needed to match thepresent spectra. We see no evidence for water ice in the availabledata. The absorption band at 3.03 J.Lmis displaced from that ofwater (3.06 J.Lm)and is narrower. If water ice is present, itcontributes little to the absorption. Similarly, solid ammonia2.91 J.Lm)is not present. Molecules involving carbon and hydro-

gen, on the other hand, can produce absorption near both 3.0and 3.4 J.Lm,and are thus particularly attractive identifications.Organic molecules containing OH and NH bonds also cause .absorption near 3.0 j.l.m(refs 6, 7). The wavelengths of CH, NHand OH vibrations depend criti~ally on the composition of the

olid and only a few cases' of astronomical interest have beendiscussed in the literature. The H bonded solid complex of H20,CH30H and NH3 (rel. 5) has a feature due to NH at 2.97 J.Lmbuthere is no correspondence with the rest of the spectrum.

It has beeo suggested recentlyS, that surface functional groupsattached to reactive sites on small carbon graina may be respon-ible for the IR features seen in IRS7. Although'there are somenteresting wavelength coincidences (aromatic -CH (3.3 J.Lm),CH3 (3.4, 3.5 J.Lm),-CHO (3.5, 3.65 J.Lmno information

has been given on band strengths and shapes to enable a detailedcomparison.

We have Ipoked at published spectra of specific grain modelsnvolving organic polymers which could be possibilities for therganic component of interstellar frains. The polymer~like

material in carbonaceous chondrites show absorption due toCH near 3.3 J.Lmand weak absorption at 3.0 J.Lm.Clearly thismaterial.will not produce a fit to the astronomical data even over

restr.icted wavelength regiolt. However, hydrated silicates o.

meteoritic origin show a broad absorption feature centred near3 J.LmlO This may be relevant in view of the possibleidentifications of the 9.7 J.Lmand 18 J.Lmfeatures in the galacticcentre with silicates. We consider it significant that the ycllowcomponent of UV tholin29 looks qualitatively similar to that ofIRS7 in the 3.4-J.Lm region: In particular the shoulder at3.36 J.Lm,the central component at 3.4 J.Lmand the componentat 3.48 J.Lmare present in the laboratory data with wavelengthsagreeing to within 0.02 J.Lm.This could indicate the existenceof complex organic molecules in grains21I.:2 However, thismaterial does not produce significant. al1sorption near 3 J.Lmas

required by the IRS7 data. It is interesting that the satellitefeatures at 3.36, 3.48 J.Lmare also seen in the spectrum ofpolyformaldehyde suggesting that H2CO may be present as astructural unie3 .

We cannot rule out the possibility that a mix of simpleorganics might match the observed spectrum. This requiresfurther investigation using laboratory data. However, as ourdata are of relevance mainly to the properties of dust in thediffuse interstellar medi um it will be more appropriate to look atrefractory materiaIs related to the UV component of tholinssuch as the non-volatile residue produced in the laboratoryexperiments dsigned to simulate conditions in the interstellarmedium described by Greenberg12 and with predictions fromthe Hoyle-Wickramasinghe modelll The latter comparison hasshown a remarkable similarity between the spectrum of IRS7and that of dried bacteria (Escherichia coli) which will bereported elsewhere'4.

Finally emission features are found in this waveband in someH 11 regions and carbon-rich planetary nebulae (for example,NGC7027) 1~. These normaiiy comprise--astrong, narrow peak at3.29 J.Lmand a weaker, broader feature peaking at 3.40 J.Lm.Inthis respect they mimic features in the relevant portion of theabsorption spectrum of IRS7. However, the 3.03 and 3.192 J.Lmfeatur~s are not seen in emission in any objects. An inter-pretation of the absorption spectrum of IRS7 which simultaneously predicted the more restricted range of the emissionbands would be very satisfying.

Recei-fed~' June; accepled 2 October 1981.

1. Wickramsinahe. D. T. & Allen. D. A. Nalu,. 28'7. 518 (1980).

2. Sa8an. C. & Khare, B. N, Nalu,. 277, 102 (1979).3. Jones. T. &Hyland. A. R. Mon. Nol. R. astr. Soe. 192, 359 (1980).4. A1lamondola, L. J. & Norman. C. A. Astr. Astrophys. 63, L23 (1978).5. Hagen W. Allamondola, L. J. & Greenberg, J. M. Astr. AJlTOphys, 86, L3 (1980).6. Herzbera, G. rnfra,.d and RanuJn S""ctrtJ of Po/yalOmic Mo~c,,~s (vau Nostrand,

Amslerdam, 1954).7. Wexler. A. S. App/. SlH'Ctrosc.Rev. I, 29 (1967).8. Duley, W. W . & Williams, D. A. Mon. Nol. R. astr. Soe. 1M, 269 (1980.9. Knaclce. R. F. Nalu,. 169, 132 (1977).

10. Knacke. R. E. & Kralschner, C. Astr. Astrophys. 92, 281 (1981).11. Hoyle, F. H. & Wickramasinghe, N C. Astrophys. Space SeL 66, 77 (1979).12. G_nbera, J. M. in 4-Io/uu~s in lhe Ga/actic EnviTOn"",nl (eds Gordon, M. & Snyder, L)

(Wiley. New Yorl

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Nature Vol. 294 19 November 1981 141

Table 1 Estimated Dvalues for various environmentalseries

"Location Property Lag Das lag . O D at max.slope Ref.

Wales Soil-sodium content IS.2m 1.7-1.9 7-.tone content IS.2m 1.1-1.8 7

(both over four direetions).England Soil-thiekness of eover loam 20m 1.6 7England Soil-electrieal resistivity (4 direetions) 1m 1.4-1.6 7England Surfaee of airport runway 30cm l.st 8Deserts in Afriea. Soil- mean cpne index -lkm . . 1.9* . - 9

and Ameriea -.ilt+elay in 0-15 em layer -lkm 1.8* 9-mean diameter of surface stones '-lkm 1.8* 9

..:...coarsesand fraction in 0-15 em layer -lkm 1.8* 9Vegetation cover -lkm 1.6* 9South Afriea ( Gold Various 1.9 2Australia Soil-phosphorus leveI Sm 2.0* 10

-pH . Sm 1.5* 10-potassium levei Sm 1.6* l.U 10-bulk density Sm I.S* 10-0.1 bar water Sm 1.5*

!10

Frane Iron ore in rocks-chlorite IS jlJJ1 1.6 11-quartz IS 110m 1.9 11-quartz Sem 1.6 . . 11-iron SCIV I.S 11-"ron (E-W) 100m 1.7 . 11-iron(N-S) 100m 1.8 11-iron (E-W) Soom 1.6 11

-iron (N-S) SOOm 1.9 11France Sea anemones tOem 1.6 12Chad' Rainfall lkm 1.7 13Mauritania Imn ore 3m 1.4 2Ivory Coast Groundwater levels

,Piezometer 1 1 day 1.6 2

2 lday 1.7 2-3 . 1 day 1.8 1.3~ 2

4 1 day 1.3 . LI 2Canada Oilgrades 60cm 1.7 2'Chile Copper grades 2m 1.7 2France Topographie heights 10m 1.S 1.1 2USA Soil-sand conte"t 10m 1.6-1.8 14

-pH 10m 2.0 14Worldwide Crop yields 1-I,ooOm 1.6-1.8* 15India -"Water table depth 250m' 1.6'* - 16

Estimated from variogram. * Estimated from bloek variance. t Estimated from power speetrum. Estimated from covarianee.

roughness. For a linear fradal fundion, the Hausdorf-Besi-covitch dimension Dmay vary between 1(completely difteren-t1able) and 1(so rough and irregular that it eftediveiy takes upthe whole of a two-dimensional topological space). For surfaces,the corresponding. range for D Iies betw41en1(absolutelyImooth) and 3 (infinitely erumpled). Because the degree ofroughness of spatial data is important when trying to makelnterpolations from point data sueh as by least-squares fiUing orkriging2, it is worth examining them beforehand to see ifthe datacontain evidence of variatiQII over difterent scales, and howImportant these seales might be. Mandelbrot's work1suggests

that the fradal dimensions of eoastlines and other linear naturalphenomena are of the order of D =1.1-1.3, implying that lo"grange efteds dominate. I show here that published data on manyenvironmental varillbles suggest that not only are they fradals,but that they may have a wide range of lradal dimensions,lncluding values that imply that interpolation mapping may notbe appropriate in certain cases. .

Berry and Lewis3 have shown that the Weierstrass-Mandel.brot fraetal functiol1' (WMF) '.

00 [(l-ei""')el"']

W(t) - 1 : 1, t f J =arbitrary phases)

has a r'wer' spectrum P(w) that varies ap-proximately' asW-

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Table 1 presents a selection of data so analysed, giving theItudy location, the type of environmental variable, the laginterval used for sampling and the estimated D value assumingthat the real data are but a series of regularly spaced samples of arealization of the Weierstrass-Mandelbrot function over one-dimensional space or time. o

The data support Mandelbrot'sl assertion that D values oflandscape and other data may range over mariy values. It isevident that most of the values reported here exceed 1.5, andmany are greater than 1.8.-Note that one of the sm